Initial States

It is important to obtain the steady state concentration of molecules in our biological circuit, since these values can be used as biologically meaningful initial conditions for subsequent simulations. To achieve this goal, we implemented a Single Cell Model. The cells plated on the game plate are from an overnight liquid culture. Thus, we assume that the cells have reached the steady state. It should be noted that the receiver cells grow in the absence of OHHL in the medium and this affects the concentrations of intracellular species whose production depends on OHHL.

Initial state for the Mine Cells

The mine colonies produce the three proteins NagZ, LuxI and OHHL, that is important in our bio-game. The proteins NagZ and LuxI are constitutively produced, whereas the synthesis of OHHL is dependent of LuxI protein. Degradation of these proteins is modeled as linear degradation. The diffusion of OHHL across the cell membrane is modeled as proposed in literature by Garcia-Ojalvo et. al., 2004.

The ODEs for the states involved in the mine cells of the system are given below:

\begin{align} \frac{d[LuxI]}{dt} =\alpha_{LuxI} - d_{LuxI} \cdot [LuxI]\\ \end{align}

\begin{align} \frac{d[NagZ]}{dt} =\alpha_{NagZ} - d_{NagZ} \cdot [NagZ]\\ \end{align}

\begin{align} \frac{d[AHL,i]}{dt}= \alpha_{AHL} \cdot [LuxI]-d_{AHL,i} \cdot [AHL,i] - \eta \cdot ([AHL,i]-[AHL,e])\\ \end{align}

\begin{align} \frac{d[AHL,e]}{dt}= -d_{AHL,e} \cdot [AHL,e] + \eta_{ext} \sum_{j=1}^{n} ([AHL,j]-[AHL,e])\\ \end{align}

System of Differential equations for a Mine Cell.

Figure 1: Steady state concentrations for Mine Cells

Initial state for the Receiver Cells

Figure 2: Steady state concentrations for Receiver Cells.

Figure 3: Steady state concentrations for Receiver Cells